Method and system for predicting wear in a rail system

ABSTRACT

A system and method is disclosed for predicting and comparing wear scenarios in a rail system. The method can include generating and running a contact model of the interaction between a rail and a train car to produce a simulated loading on the rail for a predetermined time period; generating and running a wear model based on the material properties and/or friction modifier properties of the rail using the simulated loading to produce a simulated wear profile of the rail for the predetermined time period; obtaining a grinding profile to be performed on the rail during the predetermined time period; and generating an updated rail profile by modifying the rail profile by the simulated wear profile and the grinding profile. The method can predict and compare crack growth over time, and provide a financial model and comparison of costs and benefits for different maintenance protocols for the rail system.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a non-provisional of U.S. Patent Application No.63/045,001 filed Jun. 26, 2020 entitled METHOD OF PREDICTING WEAR IN ARAIL SYSTEM, which is hereby incorporated by reference in itsentireties.

A portion of the disclosure of this patent document contains materialthat is subject to copyright protection. The copyright owner has noobjection to the reproduction of the patent document or the patentdisclosure, as it appears in the U.S. Patent and Trademark Office patentfile or records, but otherwise reserves all copyright rights whatsoever.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

REFERENCE TO SEQUENCE LISTING OR COMPUTER PROGRAM LISTING APPENDIX

Not Applicable

BACKGROUND OF THE INVENTION

The present disclosure relates generally to managing wear andmaintenance of a rail system.

More particularly, the present disclosure relates to wear caused on arail of a train track due to forces exerted into the rail by passingtrains over time. In the rail industry, a significant maintenanceexpense is incurred to maintain the rail geometry in order to maintain adesired wheel-rail interface and prevent train derailments. Over time,as the wheels pass over a rail, the stresses cause wear (physicalremoval of material) as well as cracking in the rail due to rollingcontact fatigue. The removal of the material through wear-and-teardisturbs the wheel-rail interface. Class 1 railroads spend billions ofdollars per year periodically “regrinding” the rails to reform the railto a correct or desired rail profile, and to remove any cracks formed inthe rail surface. This is a significant operational as well as logisticschallenge, because the scheduling of the rail-grinding trains has to becoordinated with the revenue-generating trains.

Today's management of grinding and maintenance operations of railsystems are limited to rail operators and maintenance crews visuallyinspecting rails for wear and defects such as cracks. Rail operators canalso consult manuals and guidelines that have been developed over timethat include recommended maintenance guidelines or indexes that arebased on compilations of observed or manually derived rail wear datawhich are at best general models of rail wear for a particular railsystem. The data used to generate these manuals or guidelines arelimited to academic studies and occasional root cause analysis aftersignificant events, e.g. derailments. Using more general wear models canlead to insufficient grinding operations being performed to maintain theproper wheel/rail interface, which can lead to dangerous operatingconditions for the rail system. Using more generalized models for railwear can also lead to unnecessary grinding operations being implemented,which can lead to faster overall wear (natural wear and grinding wear)on the rails of the train tracks. Accelerated overall wear can requirethat rail lines be replaced sooner than necessary which can increase thecosts associated with the rail lines.

What is needed then are improvements in systems and methods forpredicting wear in rail systems.

BRIEF SUMMARY

This Brief Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used as an aid in determining the scope of the claimed subjectmatter.

One aspect of the disclosure is a method for modeling wear in a rail ofa train track due to estimated train traffic. The method can includeobtaining material properties of the rail, a rail profile of the rail,and a train wheel profile of a wheel of a train car; generating acontact model of the interaction between the rail and the train carbased on the rail profile, the train wheel profile, and estimated traintraffic on the rail; running the contact model to produce a simulatedloading on the rail for a predetermined time period using the railprofile; generating a wear model based on the material properties and/orfriction modifier properties of the rail; running the wear model usingthe rail profile and the simulated loading from the contact model toproduce a simulated wear profile of the rail for the predetermined timeperiod; obtaining a grinding profile for at least one grinding operationperformed on the rail during the predetermined time period; andgenerating an updated rail profile by modifying the rail profile by thesimulated wear profile and the grinding profile.

Another aspect of the present disclosure is a method for modeling wearand crack growth in a rail of a train track due to estimated traintraffic. The method can include obtaining material properties of therail, a rail profile of the rail, and a train wheel profile of a traincar, the rail profile including a crack profile; generating a contactmodel of the interaction between the rail and a wheel of a train basedon the rail profile, the train wheel profile, and estimated traintraffic on the rail; running the contact model to produce a simulatedloading on the rail for a predetermined time period using the railprofile; generating a wear model based on the material properties and/orfriction modifier properties of the rail; running the wear model usingthe rail profile and the simulated loading from the contact model toproduce a simulated wear profile of the rail for the predetermined timeperiod; generating a crack growth model based on the crack profile;running the crack growth model using the rail profile, the crack profileand the simulated loading to produce a simulated crack growth profile ofthe rail profile for the predetermined time period; and generating anupdated rail profile with an updated crack growth profile by modifyingthe rail profile by the simulated wear profile and the simulated crackgrowth profile.

Another aspect of the present disclosure is a financial modeling thatcan help train operators make maintenance decisions for a rail systembased on a financial economic analysis associated with differentmaintenance protocols or operating scenarios. A method for modeling wearin a rail of a train track due to estimated train traffic in order toprovide maintenance recommendations for the train track, the methodincluding the steps of obtaining a train wheel profile of a train car;providing two or more sets of maintenance parameters, each set ofmaintenance parameters including: rail profile; grinding parameters; andrail material properties; wherein at least one pair of correspondingmaintenance parameters in the two or more sets of maintenance parametersis different from one another. For each of the at least two sets ofmaintenance parameters, the method can include: generating a contactmodel of an interaction between the rail profile and a wheel of a trainbased on the rail profile, the train wheel profile, and estimated traintraffic on the rail; and generating a wear model based on the materialproperties. The method can include performing a wear simulation usingthe rail profile for a predetermined time period by: running the contactmodel to produce a simulated loading; running the wear model to producea simulated wear profile based on the simulated loading; and generatingan updated rail profile by modifying the rail profile by the simulatedwear profile. The wear simulation can be repeated iteratively using theupdated rail profile and subsequent updated rail profiles until a finalupdated rail profile exceeds a predetermined wear limit for the rail.The method can include calculating a wear time until the final railprofile exceeds the predetermined wear limit, and comparing a cost valuefor each set of maintenance parameters, the cost value based onmaintenance costs associated with the corresponding set of maintenanceparameters. The method can further include recommending or selecting theset of maintenance parameters having the lower cost value.

The methods disclosed herein for modeling wear, crack growth, andgrinding can help rail operators optimize rail life by experimentingwith and modeling various aspects of the rail itself or the maintenanceprotocols associated with such rails to determine wear or rail life,without having to perform expensive and time-consuming physical orin-revenue service testing. The financial modeling methods describedherein can also help an operator optimize or balance extending wear orrail life of a rail with the costs associated with installing andmaintaining the rail to achieve that rail life.

Another aspect of the present disclosure is a computer system operableto implement the various methods described herein. The computer systemcan include an input device operable to receive various inputs andparameters, an output device for displaying information or resultsgenerated from performing the methods described herein, a memory forstoring pertinent information as well as computer-executableinstructions to implement the methods described herein via a processor.Implementing the methods disclosed herein on a computer based system canhelp an operator quickly and conveniently perform the various technicalsimulations disclosed and readily test different operating parameters inthe simulations discussed to drive their decision making process withrespect to installation and maintenance of a rail or train track system.

Numerous other objects, advantages and features of the presentdisclosure will be readily apparent to those of skill in the art upon areview of the following drawings and description of a preferredembodiment.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of one embodiment of a method ofpredicting wear of the present disclosure.

FIG. 2 is a perspective view of a train track system which can beutilized to generate a system model for the method of FIG. 1 , thesystem including a train car and a train track with rails.

FIG. 3 is a perspective view of the wheels of the train car of FIG. 2interacting with the rails of a train track.

FIG. 4 is an exemplary cross sectional view of the interface between atrain wheel of a train car and a rail of a train track system.

FIG. 5 is a perspective view of contact pressure forces from the wheelsof a train car being applied on a rail of a train track.

FIG. 6 is a schematic diagram of finite element model of a rail of traintrack system as a rolling contact pressure from the wheel of a trainpasses over the rail.

FIG. 7 a is a schematic diagram showing the effect of asperity contactor surface irregularities of the rail or train wheel on the contactpressure exerted on the rail.

FIG. 7 b is a plot of an exemplary surface pressure time history showingthe surface pressure on the rail during discrete time periods as thetrain wheel moves along the rail.

FIG. 8 is a cross sectional view showing lubricant being depositedbetween a rail and a train wheel.

FIG. 9 is a graph of surface pressure profiles on rails havingdecreasing surface roughness to show the effect of asperity contactbetween the rail and the train wheel.

FIG. 10 a is a schematic diagram of a finite element model for a rail ofa train track system which can be utilized for the simulations disclosedherein.

FIG. 10 b is a schematic diagram of another embodiment of a finiteelement model for a rail which can be used for the simulations disclosedherein, the finite element method having even smaller finite elementswithin the grain boundaries of the finite element model of FIG. 10 a tocreate a finite element mesh.

FIG. 11 is a graph of an exemplary wear simulation applied to twodifferent rail profiles over time showing an initial rail profile andsubsequent updated rail profiles creating during each iteration of awear simulation to show the wear of each of the rail profiles over time.

FIG. 12 is a plot of an initial rail profile and an updated rail profileassociated with quarter 20 of as wear simulation, the plot showingvertical and lateral rail wear limits for the rail profile.

FIG. 13 is a plot of the rail profile of FIG. 12 and a final updatedrail profile associated with a final quarter of the wear simulationwherein the final updated rail profile exceeds a vertical wear limit forthe rail profile.

FIG. 14 is a schematic view of another embodiment of a method ofpredicting wear in a rail wherein the contact model for modeling theinteraction between the rail and the train wheel is included in the wearsimulation look such that contact model can be updated with an updatedwear profile during each iteration of the wear simulation.

FIG. 15 is a schematic view of an embodiment of a method for predictionwear and crack growth in a rail system.

FIG. 16 a is a schematic view of an exemplary initial rail profile, awear profile, a crack growth profile, and a grinding profile associatedwith an iteration of a wear simulation of the present disclosure.

FIG. 16 b is a schematic view of an updated rail profile created bymodifying the initial rail profile by the wear profile the crack growthprofile, and the grinding profile.

FIG. 16 c is a detailed view of the schematic diagram of FIG. 16 ashowing an average wear depth, maximum crack growth depth, and averagegrinding depth produced from an iteration of an exemplary wearsimulation of the present disclosure.

FIG. 17 is a picture of an input interface for a financial modelingmethod of the present disclosure showing various general inputs andassumptions for the rail associated with the financial model.

FIG. 18 is a picture the input interface of FIG. 17 showing variousgrinding parameters which can be utilized for a financial modelingmethod of the present disclosure.

FIG. 19 is a picture the input interface of FIG. 17 showing variouslubrication parameters which can be utilized for a financial modelingmethod of the present disclosure.

FIG. 20 is a picture of an output of a financial modeling simulationperformed using two sets of maintenance parameters, the output showinglife extensions and costs savings values associated with the differentsets of maintenance parameters.

FIG. 21 is a schematic diagram of a financial modeling method that canbe used to compare and optimize different maintenance programs for arail.

FIG. 22 is a schematic diagram of a computer system which can beutilized to implement the various wear, crack growth and financialmodeling methods of the present disclosure.

DETAILED DESCRIPTION

While the making and using of various embodiments of the presentdisclosure are discussed in detail below, it should be appreciated thatthe present disclosure provides many applicable inventive concepts thatare embodied in a wide variety of specific contexts. The specificembodiments discussed herein are merely illustrative of specific ways tomake and use the invention and do not delimit the scope of the claimedinvention. Those of ordinary skill in the art will recognize numerousequivalents to the specific apparatus and methods described herein. Suchequivalents are considered to be within the scope of this invention andare covered by the claims.

In the drawings, not all reference numbers are included in each drawing,for the sake of clarity. In addition, positional terms such as “upper,”“lower,” “side,” “top,” “bottom,” etc. refer to the apparatus when inthe orientation shown in the drawing. A person of skill in the art willrecognize that the apparatus can assume different orientations when inuse.

Unless specifically stated otherwise, as apparent from the followingdiscussions, it is appreciated that throughout the specificationdiscussions utilizing terms such as “processing,” “computing,”“storing,” “determining,” “evaluating,” “calculating,” “measuring,”“providing,” “transferring,” or the like, refer to the action and/orprocesses of a computer or computing system, or similar electroniccomputing device, that manipulates and/or transforms data represented asphysical, such as electronic, quantities within the computing system'sregisters and/or memories into other data similarly represented asphysical quantities within the computing system's memories, registers orother such information storage, transmission or display devices.

Embodiments of the present disclosure may include a system and methodfor predicting wear and other performance factors, such as crack growth,in a rail of a train track system. Material wear, or the slow removal ofmaterial from the rail, can be caused by the active, load transmittingcontact forces applied on the rail from a wheel of a train car overtime. Rails may also degrade over time due to the formation ofmicroscopic cracks, which grow under continued usage and contact forcesapplied by the wheels of trains passing over the rail. Embodiments ofthe present disclosure may provide accurate, physics-based prediction ofwear and crack growth for rails in a train track system. Embodiments ofthe present disclosure may also provide a tool for designers and railoperators to evaluate the performance of rails in a train track systemunder a variety of scenarios (e.g., with varying materials,manufacturing processes or rail profiles, friction modifiers includingbut not limited to lubricants, operating conditions such as grindingconditions, etc.) without having to resort to expensive, time consumingtesting or other methods, and perform financial modeling to determinewhich scenario may be the most cost efficient scenario regardingmaintenance of the rails.

Embodiments of the present disclosure may consider certain aspects ofthe wear process in rail systems, the unique combination of which mayallow for a more accurate and flexible prediction of wear life in arail. For instance, consideration of friction modifier or lubricationconditions (e.g., mixed-elastohydrodynamic lubrication and otherconditions) may provide a detailed solution for surface pressures,tractions, and other loads (e.g., asperity interaction, asperitycontact) placed upon the rails of the train track system. Embodiments ofthe present disclosure may simulate or allow for simulation of therandom microstructure topology and composition in steels (e.g.,polycrystalline high strength steels other steels), composites, and/orother materials utilized for the rails based on measured materialcharacteristics and parameter distributions. Embodiments of the presentdisclosure may provide, calculate, or determine a finite elementsolution (e.g., a high fidelity finite element solution), numericalsolution, and/or analytical solution describing stress in themicrostructure of a rail of a train track system, including, forexample, highly localized near-surface contact stresses due to asperityinteraction. Embodiments of the present disclosure may predict,calculate, or determine the location and number of load cycles untilcrack nucleation and/or initiation in the grain structure of the railbeing analyzed. Embodiments of the present disclosure, may predict cracknetwork evolution through short crack growth, coalescence, on through tofailure, including possible self-arrest, or transition to long crackgrowth regime. Various other benefits may be realized from embodimentsof the present disclosure.

Wear Modeling

One aspect of the present disclosure is a method and system for modelingwear in a rail of a train track due to estimated train traffic. As seenin FIG. 1 , the method 10 can include obtaining material properties ofthe rail, a rail profile of the rail, and a train wheel profile of awheel of a train car; generating a contact model 12 of the interactionbetween the rail and the train car based on the rail profile, the trainwheel profile, and estimated train traffic on the rail; running thecontact model 12 to produce a simulated loading on the rail for apredetermined time period using the rail profile; generating a wearmodel 14 based on the material properties and/or friction modifierproperties of the rail; running the wear model 14 using the rail profileand the simulated loading from the contact model 12 to produce asimulated wear profile 16 of the rail for the predetermined time period;obtaining a grinding profile 18 for at least one grinding operationperformed on the rail during the predetermined time period; andgenerating an updated rail profile 22 by modifying the rail profile bythe simulated wear profile 16 and the grinding profile 18. In someembodiments, the method can further include the step 20 of determiningwhether the updated rail profile 22 exceeds a predetermined wear limitfor the rail. In some embodiments, the simulated wear profile 16includes a wear depth profile and generating the updated rail profile 22includes subtracting the wear depth profile from the rail profile.

In some embodiments, the method can include running a wear simulationmore than once, and can include running the contact model 12 to producea second simulated loading on the rail for a second predetermined timeperiod using the updated rail profile 22; running the wear model 14using the updated rail profile 22 and the second simulated loading fromthe contact model 12 to produce a second simulated wear profile of therail for the second predetermined time period; and generating a secondupdated rail profile by modifying the updated rail profile 22 by thesecond simulated wear profile. In some embodiments, the method caninclude obtaining a second grinding profile for a second grindingoperation performed on the rail during the second predetermined timeperiod; and generating a second updated rail profile by modifying theupdated rail profile by the second simulated wear profile and the secondgrinding profile.

In some embodiments, as shown in FIG. 1 , the method can includeiteratively performing a wear simulation 24 to determine a wear time orusable life of the rail. The method can further include performing orrepeating iteratively with the updated rail profile 22 and subsequentupdated rail profiles for corresponding subsequent predetermined timeperiods the following steps: running the contact model 12 to produce asubsequent simulated loading; running the wear model to produce asubsequent simulated wear profile based on the subsequent simulatedloading; and generating the subsequent updated rail profile by modifyingan immediately prior updated rail profile 22 by the subsequent simulatedwear profile; wherein the iteration is completed, as shown in FIGS. 11and 12 , when a final subsequent rail profile 30 exceeds a predeterminedwear limit for the rail. As such, the wear simulation 24 can be rerun insuccession using subsequent updated rail profiles 22 until thepredetermined wear limit is reached. Such a wear limit can be either avertical wear limit 26 or a lateral wear limit 26.

In some embodiments, once the wear limit is reached, the method caninclude calculating a wear time until the rail reaches a predeterminedwear limit. The wear time can be a summation of all of the predeterminedtime periods accounted for in the wear simulation, or the product of thepredetermined time period by the number of iterations of the wearsimulation performed. In some embodiments, once the wear limit isreached, the method can further include calculating an overall top weardepth, an average top wear rate, a lateral wear depth, a lateral wearrate, a combined wear depth, and a total average wear rate (an averageof the top and lateral wear rates).

For embodiments including an iterative wear simulation 24, the methodcan further include obtaining a subsequent grinding profile andgenerating the subsequent updated rail profile by updating theimmediately prior updated rail profile 22 by the subsequent wear profileand the subsequent grinding profile for at least one iteration of thewear simulation 24. As can be seen from FIG. 1 , grinding operations canbe performed in the wear simulation 24 only for a portion of thepredetermined time periods in the iterated wear simulation. Forinstance, in some embodiments, the predetermined time period can be acalendar or fiscal quarter, and grinding may only be performed in everyother quarter. In other embodiments, grinding can occur in every third,fourth, fifth, sixth, etc. quarter. In some embodiments, grinding canoccur at regulated intervals, or grinding can be spaced out more at thebeginning of the usable life of the rail and gradually increase overtime as the rail becomes more susceptible to wear and crack growth suchthat more frequent grinding can be required.

While the predetermined time period is shown in FIG. 1 as quarters, thepredetermined time period in other embodiments can be any suitable timeperiod, including days, weeks, months, quarters, years, etc. Theaccuracy of the modeling can increased with smaller predetermined timeperiods. However, in computer modeling systems, smaller time periods,and thus more iterations until the wear limit is reached, can increasethe computing requirements and time to run an iterative wear simulation.In some embodiments, as shown in FIG. 11 , the method can furtherinclude generating a plot of the rail profile, updated rail profile, andsubsequent updated rail profiles over time as the wear simulation isiterated to produce subsequent updated rail profiles. As such, the plotcan show the effect of wear and grinding on the rail and the railprofile over time.

Material properties for a rail or rail profile can include, but arelimited to, strength of the material, toughness of the material hardnessof the material, hardness of the material, brittleness of the material,friction properties of the material without lubricants or other frictionmodifiers, resilience, etc.

The wear modeling methods described herein can be utilized by railoperators and installers to model the wear life of contemplated railsystems. The modeling method can also be utilized to help maximize oroptimize the wear life of a rail system. For instance, different railprofiles 46 can be investigated using the various methods disclosedherein as shown in FIG. 11 to model and predict which rail profile 46can provide longer wear life. Variations in grinding parameters such asthe frequency of grinding operations and the depth of the grindingoperations can also be modeled independently to determine which grindingparameters maximize or optimize wear life.

In some embodiments, the contact model further includes a system model12 a of the interface between the train car 34 and the train track 36and a wheel contact model 12 b of the interface between the wheel 38 ofthe train car 34 and the rail 40, the train track 36 including multiplerails 40 connected to one another by rail ties and fasteners. As shownin FIGS. 2-3 , in conventional train cars 34, at least two sets of trainwheels 38 can be included on each train car 34. A front set of wheels 42can have different force and pressure profiles, as well as differentlocations on the rail 40 where such forces or pressure profiles can beapplied, than the back set of wheels 44 as the train car 34 passes overthe rail 40. This can be particularly true on curved track segments asfront wheels 42 initiating a turn on the rail 40 may exert differentforces on the rail 40 and at different locations compared to the forcesexerted by the back wheels 44 of a train car 34 completing the turn. Thesystem model 12 a can account for these different pressure profiles andpressure locations on the rail 40 between different sets of wheels 42,44 on the train car 34 and provide a system model 12 a of the forcesacting on the rail 40 by an entire train car 34 and not just one wheel38. Train traffic can then be quantified in the contact model 12 as thenumber of train cars 34 passing over the rail 40 in a predetermined timeperiod. In some embodiments, the system model 12 a can include theVampire® Vehicle-Track Interface modeling and simulation software.However, any suitable modeling program or software can be utilized as asystem model 12 a to sufficiently model the interface between the traincar 34 and the train track 36.

The wheel contact model 12 b can apply the different contact forces fromthe system model 12 a and apply them as rolling contact forces onto thegeometric interface between a train wheel profile 46 and a rail profile48, shown in FIG. 4 , or updated rail profiles produced during aniterative wear simulation. The wheel contact model 34 in someembodiments can include the CONTACT™ wheel-rail interface softwareprovided by VORtech CMMC. In other embodiments, any suitable wheelcontact modeling simulation or software can be used for the wheelcontact model 12 b. The combination of the system model 12 a and thewheel contact model 12 b can be used to produce a simulated loading onthe rail 40 which takes into account overall system forces of the traincar 34 on the rain track 36 as those forces are applied to the interfacebetween the train wheels 38 and the rail 40 of the train track 36.

In some embodiments, as shown in FIG. 14 , generation of the contactmodel 12 can be included in the wear simulation loop 24, such that themethod 10 can further include regenerating the contact model 12 of theinteraction between the rail and a train based on the updated railprofile 22, the train wheel profile, and estimated train traffic on therail; running the contact model 12 to produce a second simulated loadingon the rail for a second predetermined time period using the updatedrail profile 22; running the wear model 14 using the updated railprofile 22 and the second simulated loading from the contact model 12 toproduce a second simulated wear profile of the rail for the secondpredetermined time period; and generating a second updated rail profileby modifying the updated rail profile by the second simulated wearprofile. In embodiments including an iterative wear simulation, thecontact model 12 of the interaction between the rail and a train can beregenerated for each iteration of the wear simulation 24 utilizing theupdated rail profile 22 and each subsequent updated rail profile untilthe simulation is ended. Second or subsequent grinding profiles can beincluded in one or more iterations of such iterated wear simulations 24.Having the contact model 12 be regenerated during more than one and/oreach iteration of the wear simulation 24 can help provide a more refinedsimulated loading model over time. As the rail profile changes overtime, so will the loading characteristics between the train car and/orwheels of the train and the rail. Updating the contact model 12 can helpmore accurately model the wheel/rail interface over time and produce amore accurate wear model 14 for the rail.

In some embodiments, generating the contact model includes generating afinite element model based on the material properties of the rail,wherein the finite element model describes a grain structure of the railand represents crystalline or polycrystalline properties of the rail, asshown in FIGS. 10 a and 10 b . In some embodiments, a finite elementmodel may include a numerical technique which may be used to determinethe response of a volume of material utilized for the rail to an appliedloading situation, the finite element model subject to constitutive orconnective relationships and boundary conditions. The material volume ofthe rail can be discretized by a complex system of points or nodes thatdefine discrete elements of the material volume, as shown in FIGS. 10 aand 10 b . By defining basis functions for each element and utilizing aconstitutive or connective relationship to define the elastic/plasticbehavior of the material, a finite element model can be used whichincorporates a system of algebraic equations for the finite elementmodel, which may be solved using conjugant gradient or other methods.

A random micro-structure instance 120 for the rail may be calculated,created or generated as part of the contact model. The randommicrostructure instance 120 may serve as a finite element modeldescribing or modeling the grain structure of the rail 40 to beanalyzed. A finite element model may be a group or series of discreteequations or data points that are related to each other. The finiteelement model describing the material grain structure of the rail 40 mayrepresent the rail's crystalline or polycrystalline properties. A finiteelement model may be generated to account for various materialproperties associated with different materials that be used for therail. Information pertaining to the particular material (e.g., materialspecimen) of interest, out of which a rail can be made, may be gathered,downloaded and or input into the computer system 100.

In some embodiments, information pertaining to the material of interestmay be gathered by a person through either physical examination viaoptical microscopy and/or scanning electron microscopy of samplematerial specimens obtained from the component of interest or via asurvey of published material properties found in the open literature orthrough some combination thereof. Information may, for example, be agathered by user through physical examination of a specimen pf the railusing, for example, a microscope (e.g., an optical microscope, electronmicroscope, scanning electron microscope), physical inspection (e.g.,visual, tactile, etc.), or other type of inspection. Data or informationrelating to the rail may, for example, be obtained or gathered frompublished material properties, e.g., found in the open literature (e.g.,journals, textbooks, publications, etc.), electronic databases, or othersources. Data describing the statistical distributions of both thegeometric features and physical composition of the microstructure for agiven material may be assembled, combined, or aggregated by a person,system, or processor associated with the computer system 100 (e.g.,processor 102) into one or more data files. The one or more data filesmay be used throughout the simulation process. A memory 104 or otherstorage device may store these material properties.

Utilizing information such as size, composition, and otherdistributions, an instance 120 of a random polygonal (e.g., polyhedralor other shape) crystalline structure may be generated by system 100(e.g., by processor 102) using a Voronoi tessellation 110 or othersuitable process. The Voronoi tessellation process may include fillingthe domain or space of interest with randomly placed nucleation points122 or seed points, consistent with microstructure geometric informationgathered, provided, or generated. Nucleation points 122 may be localizedareas within a crystal or crystalline material that exhibit a distinctthermodynamic phase. The nucleation points may create the grainstructure of the rail 40. Different materials may have differentnucleation characteristics and grain structure due to the atomicstructure or manufacture of the materials. For example, the number ofnucleation points 122 per volume in a material may depend on thecrystallization process used, the solute concentration or suspensiondensity of the crystal solute used in the material. The randomly placednucleation points 122 may simulate or represent the geometric or otherinformation input into system 100. Regions may be constructed orgenerated around each nucleation point such that all points enclosed bythe region are closer to that particular nucleation point 122 than anyother nucleation point in the domain. The resulting regions may beconvex polygons (e.g., polyhedra or other shapes) each, for example,representing an individual grain in the microstructure. Randomdistribution of the nucleation points 122 may help provide topologicalrandomness in the microstructure. System 100 may, in some embodiments,store the description of the Voronoi tesselation in the database 112(e.g., in a data file), which may, for example, include Cartesiancoordinates for each nucleation point, Cartesian coordinates for eachcorner (e.g., vertex) of the polygons (e.g., polyhedra), and/or a listof vertices associated with each seed point. A table, hash table, map,or other data structure may include nodes that represent these verticesand nucleation points 122, and may also describe the relation orconnectivity between each node.

According to some embodiments, the Voronoi tessellation, nowrepresenting or simulating the microstructure (e.g., grainmicrostructure) of the material specimen (e.g., steel material presentin high strength steels or other materials), may serve as the finiteelement model, or may be further discretized or meshed into smallerfinite elements 128 to form a finite element mesh by system 100 usingtriangular, tetrahedral or other shaped elements. The finite elementmesh may also be based on the material properties of the rail 40. Theresulting meshed domain may be an instance of a random microstructurerepresentative volume. System 100 may store the description of the meshin a data file (e.g., stored in memory 104, database 106, etc.)containing Cartesian coordinates of the nodes 122 and connectivityinformation to define the triangular or tetrahedral elements from thenodes 122.

According to some embodiments, as shown in FIG. 7 a , a finite elementmodel describing or modeling stresses in the microstructure or grainstructure may be determined for each load event or loading cycle of asimulated loading 130 for a predetermined time period onto the finiteelement model, e.g., random microstructure instance 122. In a traintrack system, a loading event or loading cycle of the simulated loading130 can be the passage of a single wheel of a train car or the passageof all wheels of a train car over the rail. Depending on the estimatedtrain traffic occurring on a particular rail being analyzed, the numberof load cycles occurring within a predetermined time period can vary indifferent simulated loading 130. Stresses in the finite element modelfor a loading event in some embodiments may be calculated or determinedin response to an externally calculated surface pressure time history132 which may be read or input into system 100. A surface pressure timehistory 132 may describe or model the loading boundary conditionsdescribing a single load event in sequential time steps 134, 136, 138.Surface pressure 140 may include surface traction and bulk load exertedon the rail 40 during a load event, or contact by a wheel of a train.Surface traction may be the frictional forces exerted on a rail'ssurface due to surface roughness, as the rail 40 interacts with thewheel of a train. Bulk load may be the external load forces experiencedby the rail as the wheels apply rolling contact pressure to the rail 40.Surface pressure 140 in some embodiments may include other types offorces and loads acting on the rail.

In some embodiments, loading events of the simulated loading 130 can bedivided into discrete time steps, and a defined load of the loadingevent can be simulated to travel a distance over the rail 40 in eachtime step 134, 136, and 138, wherein the defined load is simulated toexert different amounts of pressure 140 across the rail 40 in each timestep due to asperity contact between the rail 40 and the wheel of thetrain car. The surface pressure time history 132 may represent the loadsor pressures 140 exerted on the rail 40 at each time period or episode134, 136, or 138. The surface pressure time history 132 may, forexample, be the output of a surface pressure analysis. Surface pressureanalysis may predict, determine or define loads (e.g., stresses, shearstresses, pressures, etc.) acting on a surface of a rail 40, an area ofcontact (e.g., between the rail 40 and the train wheel), and otherparameters. Surface pressure time history 132 may, for example,represent a traction load event applied to a rail 40 when the rail 40 iscontacted by the train wheel. Surface pressure time history 132 may, forexample, be determined or calculated based on one or more loadingparameters. Loading parameters can be related to the geometry, physicalproperties of the rail 40, operating conditions (e.g., environmentalconditions, etc.), friction modifier parameters or properties (e.g.,rail lubricants, wheel lubricants, other lubricants between the rail 40and train wheels, rail surface finish, and/or other loading parameters.Loading values, factors or parameters can include in some embodiments asurface roughness profile, lubricant properties, surface velocities,curvatures, transmitted load, and other parameters.

Surface velocities can represent the relative linear or angularvelocities of the wheels on the rail 40 during traction loading.Curvatures can represent or define the surface geometry of the rail(rail profiles or updated rail profiles). Transmitted loads mayrepresent the load (e.g., force, pressure, etc.) applied to the rail 40.

The surface pressure time history 132 may be determined or calculatedbased on one or more loading parameters using numerical methods or othermathematical approaches. In a surface traction analysis, loadingparameters (e.g., surface roughness profile, lubricant properties, etc.)may be used to explicitly calculate or determine a detailed solution forpressure and shear stress acting on the surface of the rail 40 and areaof contact due to load supported by both lubrication (e.g., alubrication fluid film) and direct material contact (e.g., asperitycontact).

Surface pressure time history 132, which may include bulk loading timehistory and surface traction time history can be calculated a-priori(e.g., using processor 102), typically utilizing results from amacro-level finite element model of the rail 40. Surface traction timehistory and bulk loading time history may be used by the system 100 todetermine or define boundary conditions on the finite element model forthe rail 40. Boundary conditions may be assigned by system 100 (e.g.,based on surface traction history, bulk loading time history, and/orother parameters) to constrain nodal degrees of freedom on theboundaries of the representative volume domain. The boundary conditionsmay also limit the effect that some nodes of the microstructure instance122 may have on other nodes.

FIGS. 6 and 9 demonstrate the effect of asperity contact between therail 40 and the wheel of a train. Irregularities or increased surfaceroughness in the surfaces of the rail 40 and/or the train wheel canlocalized surface pressures to increase as forces and thus pressures arelocalized to the surface irregularities. In some embodiments, thedefined loads of the simulated loading are simulated to exert differentamounts of pressure across the rail in each time step due to asperitycontact between the rail and the wheel of the train car.

Referring again to FIG. 1 , the wear model 14 can include any suitablemodel for calculating wear, or a volume of material removed from therail due to forces acting upon the rail by a passing train wheel. Insome embodiments, wear can be calculated utilizing the generalizedformula below:

$\begin{matrix}{Q = \frac{KWL}{H}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$

In Equation 1, Q is the total volume of wear debris produced, K is adimensionless constant and can include the coefficient of friction, W isthe total normal load applied on the rail, L is the sliding distance orcontact area, and H is the hardness of the contact surface. Thisequation or wear model can in some embodiments be applied to the finiteelement model of the rail 40 to determine a wear on individual grainstructures of the rail such that an overall wear profile 16 can beproduced utilizing the wear model 14. The wear profile 16 can be atwo-dimensional or three-dimensional wear profile in some embodiments.Any other suitable wear model 14 can be utilized to simulate wear on therail due to a simulated load on the rail.

The wear model can also take into account friction modifier propertiesof the rail, which can affect the coefficient of friction for aparticular system. If the rail is coated with lubricant for instance, itcan reduce the coefficient of friction between the rail and the trainwheel thus reducing the wear produced on the rail by the train.Different lubricants can produce different lubrication or frictionmodifier properties can be factored into the wear model accordingly.

On a first iteration of the wear simulation loop, the original railprofile can be modified by the wear profile 16 produced for the initialpredetermined time period in order to produce an updated rail profile22. The updated rail profile and subsequent updated rail profiles canthen be fed back into the contact to multiple to produce subsequentsimulated loadings, subsequent wear profiles, and subsequent updatedrail profiles until the wear on the rail compared to the original railprofile exceeds a predetermined limit, indicating the end of the wearlife for the rail, as shown in FIG. 11 .

The methods for calculating wear in a rail of a rail or train tracksystem disclosed herein can be utilized to determine wear life in a railhaving a particular rail profile, loading characteristics, frictionmodifier properties, grinding schedule (artificial wear), materialproperties etc. as described herein to help more accurately determinewhen a rail may need to be replaced. The method of predicting wear inthe present disclosure can also be utilized to compare differentoperating conditions in a rail system, including a variation in railprofiles, loading characteristics, friction modifier properties,grinding schedules (artificial wear), material properties, etc. todetermine which operating conditions may increase wear life in a railsystem.

Wear and Crack Growth Modeling

Another aspect of the present disclosure, as shown in FIGS. 15-16 is amethod for modeling wear and crack growth in a rail 40 of a train trackdue to estimated train traffic. The method can include obtainingmaterial properties of the rail 40, a rail profile 48 of the rail 40,and a train wheel profile of a train car, the rail profile including aninitial crack profile; generating a contact model 12 of the interactionbetween the rail 40 and a wheel of a train based on the rail profile 48,the train wheel profile, and estimated train traffic on the rail;running the contact model 12 to produce a simulated loading on the rail40 for a predetermined time period using the rail profile; generating awear model 14 based on the material properties and/or friction modifierproperties of the rail 40; running the wear model 14 using the railprofile 48 and the simulated loading from the contact model 12 toproduce a simulated wear profile 16 of the rail 40 for the predeterminedtime period; generating a crack growth model 50 based on the railprofile 48; running the crack growth model 50 using the rail profile 48and the simulated loading to produce a simulated crack growth profile 52for the rail profile 48 for the predetermined time period; andgenerating an updated rail profile 22 with an updated crack profile 56by modifying the rail profile by the simulated wear profile 16 and thesimulated crack growth profile 52.

In some embodiments, the rail 40 may not initially include any crackssuch that the crack profile of the rail profile 48 would not include anycracks, and running of the crack growth model 50 will determine whetherone or more cracks 54 will form or be initiated in the rail 40 duringthe predetermined time period, and if so how deep those cracks 54 mayget. If no crack formation is predicted during the predetermined timeperiod, the simulated crack growth profile 52 can additionally notinclude any cracks, and thus the rail profile 48 would only be modifiedby wear via the wear profile 16 on the rail 40, and not crack growth,and the updated rail profile 22 and the updated crack profile would notinclude any cracks.

In other embodiments, the crack growth model 50 may indicate formationof cracks 54 in the rail profile 48 during the predetermined timeperiod, such that the simulated crack growth profile 52 may include theformed or initiated one or more cracks 54. In some iterations of thewear simulation 24, any wear experienced in the rail 40 may remove someor all of the one or more cracks 54 formed in the rail 40 during thepredetermined time period. In other iterations, the crack growth mayoutpace the wear in the rail 40, such that an updated rail profile 22accounting for both the simulated wear profile 16 and the crack growthprofile 52 may include small left over cracks, such that an updatedcrack profile 56 in the updated rail profile 22 includes one or morecracks. As shown in FIGS. 16 a-16 c , the simulated crack growth profile52 would include fromed cracks 54 extending from the rail profile 48into the rail 40.

In still other embodiments, an initial rail profile 48 may include aninitial crack profile 58, and the crack growth model 52 can calculatethe formation of any new cracks 54 and the additional crack growth 60 orpropagation of the initial crack profile 58, and the simulated crackgrowth profile 52 can include both new cracks 54 and the growth 60 ofthe initial crack profile 58, as shown in FIG. 16 c.

Referring again to FIGS. 15-16 , in some embodiments, the method canfurther include performing a wear simulation 24 by repeating orperforming iteratively with the updated rail profile 22 with the updatedcrack profile 52 and subsequent updated rail profiles with subsequentupdated crack profiles for corresponding subsequent predetermined timeperiods the following steps: running the contact model 12 to produce asubsequent simulated loading; running the wear model 14 to produce asubsequent simulated wear profile based on the subsequent simulatedloading; running the crack growth model 50 to produce a subsequentsimulated crack growth profile; and generating the subsequent updatedrail profile with the subsequent updated crack profile by modifying animmediately prior updated rail profile by the subsequent simulated wearprofile and the subsequent simulated crack growth profile; wherein themethod is completed when a final subsequent rail profile exceeds apredetermined wear limit for the rail or a final updated crack profileexceeds a predetermined crack growth fail limit. As such, a wear andcrack growth simulation 24 can be run on a rail profile 48 to model bothwear and crack growth over time and determine when a rail 40 will eitherreach a wear fail limit or a crack growth fail limit and need to bereplaced.

It can be beneficial to model both wear and crack growth on a railsimultaneously. While crack growth can be modelled over time to show thegrowth or expansion of a crack or defect in the rail, wear from thetrain can reduce the general depth of crack growth similar to the waywear can reduce the depth of the rail generally. As such, wear can slowdown crack growth in some circumstances. In other circumstances giventhe orientation or angle of the crack, wear can exacerbate crack growth.As such, a crack growth prediction method that does not account for wearmay not be sufficient to accurately predict rail failure due to crackgrowth, which can either cause a rail to be replaced prematurely or notbe replaced when necessary to maintain safe operating conditions.

In some embodiments, propagation of an existing crack can be modelled bythe following generalized differential equation:

$\begin{matrix}{{\frac{da}{dN} = {f\left( {{\Delta\sigma},a,C_{i}} \right)}},} & {{Eq}.\mspace{14mu} 2}\end{matrix}$

Wherein the crack length is denoted as a, the number of cycles is givenby N, the stress range by Δσ, and the material parameters by C_(i). Insome embodiments, any suitable different equation for the crack growthmodel 50 can be utilized, including but not limited to one or more ofthe Paris Erdogan equation, the Forman equation, the McEvily-Groegerequation, the NASGRO equation, the McClintock equation, the Walkerequation, or the Elber equation. In some embodiments, calculation andprediction of the formation of cracks 54 in the rail 40 and the growthof those cracks over time via the crack growth model 50 can utilize themethods taught in U.S. Pat. No. 10,474,772, which is incorporated hereinby reference in its entirety.

In some embodiments, the method can further include obtaining a grindingprofile 18 for at least one grinding operation performed on the rail 40during the predetermined time period; and generating the updated railprofile 22 by modifying the rail profile 48 by the wear profile 16, thecrack growth profile 52, and the grinding profile 18. FIGS. 16 a-16 cshows an initial rail profile 48 with an initial crack profile 58. Assuch, the updated rail profile 22 can be produced by overlaying thecrack growth profile 52 and the wear profile 16 onto the rail profile48. Grinding operations can further reduce rail material around thecrack and reduce the amount of crack growth, or remove material aroundlocal crack growth in a predetermined time period. As shown in FIGS. 16a-16 c , the rail profile 48 can be modified by the crack growth profile52 during the predetermined time period, which can be mitigated by thewear profile 16 in the rail and the further grinding of the rail 40,represented by the grinding profile 18 during the predetermined timeperiod to produce an updated rail profile 22 with an updated crackprofile 56.

In some embodiments, grinding operations can be designed to completelyremove all formed cracks in the rail in a predetermined time period toslow crack growth as much as possible. In other embodiments, grindingoperations can be designed to remove only a portion of the crack growthnot removed by natural wear. Grinding produces artificial wear in therail 40 that can reduce the wear life of the rail. As such, in someembodiments, grinding may be designed to remove a minimum amount ofcrack growth so that the rail 40 does not proceed to crack growthfailure, or so the rail keeps an acceptable amount of cracks and/orcrack growth in the rail 40 over time. As such, both wear life and crackgrowth failure life can be optimized. The method of modeling wear andcrack growth with additive grinding can help a rail operator modelvarious operating scenarios to determine the optimum conditions tooptimize wear as well as crack failure life.

In some embodiments, for each iteration, the method can includeregenerating the contact model 12 of the interaction between the railand a train based on the updated rail profile 22 including the updatedcrack profile 56, as well as subsequent updated rail profilescorresponding subsequent updated crack profiles, the train wheelprofile, and estimated train traffic on the rail. Regenerating thecontact model 12 during each iteration can help provide a more accuratesimulation of loads on the rail and as the rail profile and the crackprofile change over time. In some embodiments, the method can furtherinclude generating a plot of the rail profile with the crack profile,the updated rail profile with the updated crack profile, and subsequentupdated rail profiles with the subsequent updated crack profiles overtime.

In some embodiments, the wear profile 16 can include an average weardepth 62, and the crack growth profile can include a maximum crackgrowth depth 64, and the method further comprises calculating arecommended grinding profile having an average grinding depth 66substantially equal to the difference between the maximum crack growthdepth 64 and the wear depth 62. As such, grinding can generally beincorporated into the rail maintenance operations to remove any cracksformed in the rail over time to help slow any crack propagation in therail 40.

In some embodiments, as the contact model, the wear model, and the crackgrowth model are all physics-based models. The physics based models foreach of these components has been discussed previously herein.

The crack growth modeling aspects of the present disclosure can also beincorporated into the computer system 100 discussed previously hereinand as shown in FIG. 21 . The input device 108 can further be operableto receive a rail profile including a crack profile. The computerreadable instructions executed by the processor 102 can further beconfigured to generate a crack growth model based on the rail profile;running the crack growth model using the rail profile and the simulatedloading to produce a simulated crack growth profile of the rail for thepredetermined time period; and generating an updated rail profile bymodifying the rail profile by the wear profile and the crack growthprofile.

In some embodiments, the input device 108 can be operable to receive agrinding profile of at least one grinding operation to be performedduring the predetermined time period; and predicting wear via thecomputer system 100 can further include generating the updated railprofile by modifying the rail profile by the wear profile, the crackgrowth profile, and the grinding profile.

In some embodiments, the updated rail profile includes an updated crackprofile, and the computer readable instructions cause the processor 102to repeat iteratively with the updated rail profile with the updatedcrack profile and subsequent updated rail profiles with subsequentupdated crack profiles for corresponding subsequent predetermined timeperiods the following steps: running the contact model to produce asubsequent simulated loading; running the wear model to produce asubsequent simulated wear profile based on the subsequent simulatedloading; running the crack growth model to produce a subsequentsimulated crack growth profile; and generating the subsequent updatedrail profile with the subsequent updated crack profile by modifying animmediately prior updated rail profile by the subsequent simulated wearprofile and the subsequent simulated crack growth profile; wherein themethod is completed when a final subsequent rail profile exceeds apredetermined wear limit for the rail or the crack profile exceeds apredetermined crack growth fail limit.

Financial Modeling

Another aspect of the present disclosure is a financial modeling thatcan help train operators make maintenance decisions for a rail systembased on a financial economic analysis associated with differentmaintenance protocols or operating scenarios. A method for modeling wearin a rail of a train track due to estimated train traffic in order toprovide maintenance recommendations for the train track, the methodincluding the steps of obtaining a train wheel profile of a train car;providing two or more sets of maintenance parameters, each set ofmaintenance parameters including: rail profile; grinding parameters; andrail material properties; wherein at least one pair of correspondingmaintenance parameters in the two or more sets of maintenance parametersis different from one another. For each of the at least two sets ofmaintenance parameters, the method can include: generating a contactmodel of an interaction between the rail profile and a wheel of a trainbased on the rail profile, the train wheel profile, and estimated traintraffic on the rail; and generating a wear model based on the materialproperties. The method can include performing a wear simulation usingthe rail profile for a predetermined time period by: running the contactmodel to produce a simulated loading; running the wear model to producea simulated wear profile based on the simulated loading; and generatingan updated rail profile by modifying the rail profile by the simulatedwear profile. The wear simulation can be repeated iteratively using theupdated rail profile and subsequent updated rail profiles until a finalupdated rail profile exceeds a predetermined wear limit for the rail.The method can include calculating a wear time until the final railprofile exceeds the predetermined wear limit, and comparing a cost valuefor each set of maintenance parameters, the cost value based onmaintenance costs associated with the corresponding set of maintenanceparameters. The method can further include recommending or selecting theset of maintenance parameters having the lower cost value. The contactmodel and wear model can be similar to those contact and wear modelsdiscussed previously herein.

The cost value associated with each set of maintenance parameters caninclude capital costs, depreciation (inversely proportional to wear orrail life of the rail), and maintenance costs. Depreciation can beclosely tied to the cost savings associated with prolonging thereplacement of an existing rail with a new rail. Longer wear or raillife of the rail can help extend the time period before a rail lineneeds to be replaced, which can thus spread out the depreciation costsor the rail due to wear and other damage over a longer period of timeand reduce an annual depreciation of the rail. Varying differentmaintenance parameters can affect either the capital costs,depreciation, or maintenance costs as discussed in more detail herein.

In some embodiments, as shown in FIG. 17 , the financial model caninclude an analysis of a desired segment of the train track or a certainnumber of miles of a train track, and the at least two sets ofmaintenance parameters can each include percentages of the train trackthat are: straight track segments; mild curved track segments; andsevere curve track segments. Capital costs and wear rates can varydepending on whether track segments are straight, mildly curved, orseverely curved.

In some embodiments, the grinding parameters can include a grindingprofile for a desired grinding operation performed during one or moreiterations of the wear simulation; and the method can further include,for the one or more iterations of the wear simulation where grinding isperformed, generating the updated rail profile by modifying the railprofile or an immediately prior updated rail profile by the simulatedwear profile and the grinding profile.

In some embodiments, as shown in FIG. 18 , the grinding parameters caninclude one or more of: a grinding frequency (or the number of overallgrinding operations), a grinding speed; a grinding depth; or a number ofgrinding passes in each grinding operation. The grinding or reprofilingspeed can be inversely proportional to the grinding depth created in agrinding pass, as a slower speed of a grinding machine can cause morematerial to be removed as the grinding machine proceeds down the rail.In many grinding machines, the angle of the grinder can be adjusted,such that multiple grinding passes can be performed with the grindingmachine at different angles so that the grinding machine may be able tomore closely match or conform to the shape of a reprofiled rail, or theupdated rail profile, to a desired or optimal rail profile. The numberof corrective grinding passes shown in FIG. 18 can be proportional tothe conformity of the updated rail profile to a desired rail profile.Conformity to a desired rail profile can help optimize wear life in arail system, and thus decrease annual depreciation of the rail acrossthe usable life of the rail. Total grinding costs, including associatedrental, labor cost, and potential train track downtime costs associatedwith the grinding parameters, can also increase proportionally to thenumber of grinding passes, and inversely to the speed and thus the depthof each grinding pass. As such, while changing certain grindingparameters can help increase wear life, and thus decrease annualdepreciation and capital replacement costs of the rail, savingsassociated with increased wear or rail life can be balanced or offsetvia the financial model. Inversely, reducing grinding operations maydecrease grinding maintenance costs but may reduce wear life and thusincrease annual depreciation.

Similarly, capital costs can include the costs of the rail materials andmanufacturing of the rails. Some materials may have greater resistanceto wear, and thus increase wear life, but thus stronger materials may bemore expensive to purchase, so the increase in capital costs mayoutweigh the savings associated with longer wear life, or vice versa.

As seen in FIG. 19 , in some embodiments, each set of maintenanceparameters also includes friction modifier parameters. In someembodiments, the friction modifier parameters can include a distancebetween friction modifier applicators on the train track; a number offriction modifier applicators; the uptime of friction managementapplications; the effectiveness of friction management applicator, orfriction modifier material properties. As noted previously herein,friction modifiers such as lubricants can help reduce wear between therail and the train wheel, which can thus increase wear life. Thus, thewear model can be based off of material properties of the rail and/orlubrication properties of the rail. The greater the distance betweenfriction modifier applicators on the rail, the lower the uptime of thefriction management applicators, or the lower effectiveness of frictionmanagement applicators, resulting in a higher risk that the frictionmodifier is not applied to the entire rail, which can increase the wearon the rail. The number of friction modifier applicators and theparticular friction modifier or lubrication properties of frictionmodifiers can also affect the degree to which the friction modifier(s)can reduce wear and increase wear life of the rail. However, thefriction modifier stations can increase maintenance costs, and the costssavings associated with increased wear life can be offset or balanced bythe increased cost of more frequent lubrication stations.

In some embodiments, the financial modeling method disclosed herein caninclude welded train tracks, and the at least two sets of maintenanceparameters each include welding parameters. Welding parameters canaffect operating expenses the rail during its life cycle.

In some embodiments, the method can further include modeling crackgrowth as well as wear in the rail over time and accounting for suchcrack growth in the financial analysis. In such embodiments, in each setof maintenance parameters, the rail profile can include a crack profile,and for each set of the at least two sets of maintenance parameters, themethod further includes generating a crack growth model based on therail profile and the crack profile, and the wear simulation furtherincludes running the crack growth model using the rail profile, thecrack profile and the simulated loading to produce a simulated crackgrowth profile for the predetermined time period; and generating anupdated rail profile with an updated crack profile by modifying the railprofile by the simulated wear profile and the crack growth profile,repeating the wear simulation iteratively using the updated rail profileand subsequent updated rail profiles until a final updated rail profileexceeds a predetermined wear limit for the rail or the updated crackprofile exceeds a predetermined crack growth fail limit; and calculatinga wear time until the final rail profile exceeds the predetermined wearlimit or the updated crack profile exceeds a predetermined crack growthfail limit.

In some embodiments, the financial modeling method discussed herein canbe implemented on the computer system 100 described herein and shown inFIG. 21 . The method can further include configuring a computer-basedsystem 100 to predict and compare wear or rail life in the rail of thetrain track and provide cost value estimates associated with at leasttwo sets of maintenance parameters, the computer-based system 100including an input device 108 operable to receive a train wheel profileand the at least two sets of maintenance parameters; an output device110 operable to convey wear and cost value information relating to therail; memory 104 operable to store a train wheel profile of a wheel of atrain car and the at least two sets of maintenance parameters, andcomputer-executable instructions including wear prediction processes;and a processor 102. The method can include predicting and comparingwear and rail life scenarios in the rail for each of the at least twosets of maintenance parameters with the computer-based system 100according to the wear prediction processes of the computer-executableinstructions, wherein the computer-executable instructions cause theprocessor 102 to predict wear in the rail by: generating a contact modelof an interaction between the rail profile and a wheel of a train basedon the rail profile, the train wheel profile, and estimated traintraffic on the rail; and generating a wear model based on the materialproperties. The computer system 100 and the processor 102 caniteratively perform the various wear simulations discussed herein foreach set of maintenance parameters until a final updated rail profileexceeds a predetermined wear limit for the rail or a crack growthprofile exceeds a crack growth limit. The computer based system can thencalculate a wear time until the final rail profile exceeds thepredetermined wear limit; and calculate via the processor a cost valuefor each set of maintenance parameters, the cost value based onmaintenance costs associated with the corresponding set of maintenanceparameter.

As shown in FIG. 21 , the output device 110 can include a user interfacewhich can be operable to display one or more graphs of the cost valuesfor each set of maintenance parameters, as well as provide a costsavings calculation between the at least two sets of maintenanceparameters. As such once wear and/or crack growth simulations areperformed for each set of maintenance parameters and calculate costvalues for the same, the output device 110 can display such informationin a format such that the user can readily compare the results of theexecuted simulations and costs analysis.

While wear and crack growth simulations alone can be utilized to helpmaximize or optimize wear life or crack growth failure life, often timesthe value saved by extended the life of the rail may not justify thehigher costs associated with achieving that rail life extension. Afinancial model can help a rail operator account for and optimizemaintenance parameters to achieve the optimal balance of rail lifeextension and maintenance costs which provide the largest overalleconomic savings to the rail operator.

Thus, although there have been described particular embodiments of thepresent invention of a new and useful METHOD OF PREDICTING WEAR IN ARAIL SYSTEM, it is not intended that such references be construed aslimitations upon the scope of this invention.

What is claimed is:
 1. A method for maintaining a train track, themethod comprising: modeling a plurality of predicted rail profiles of arail based on a plurality of sets of maintenance parameters, each set ofthe plurality of sets of maintenance parameters associated with arespective predicted rail profile of the plurality of predicted railprofiles, each set of the plurality of sets of maintenance parametersincludes different maintenance parameters, the maintenance parametersincluding at least one of a grinding profile for at least one grindingoperation to be performed on the rail to produce artificial wear or anapplication of a friction modifier to be applied to the rail, whereinmodeling each of the plurality of predicted rail profiles comprises:modeling wear in the rail due to estimated train traffic and the set ofmaintenance parameters over an initial predetermined time period by:obtaining material properties of the rail, a rail profile of the rail,and a train wheel profile of a wheel of a train car; generating acontact model of the interaction between the rail and the train carbased on the rail profile, the train wheel profile, and the estimatedtrain traffic on the rail during the predetermined time period; runningthe contact model to produce a simulated loading on the rail for thepredetermined time period using the rail profile, wherein the simulatedloading represents a passage of the wheel of the train car; generating awear model based on the material properties and/or properties of thefriction modifier on the rail during the predetermined time; running thewear model using the rail profile and the simulated loading from thecontact model to produce a simulated wear profile of the rail for thepredetermined time period, wherein the simulated wear profile representsthe rail of the train track; and generating an updated rail profile bymodifying the rail profile by the simulated wear profile and thegrinding profile; and determining whether the updated rail profileexceeds a predetermined wear limit for the rail; and iterativelymodeling wear in the rail over subsequent predetermined time periodsuntil the updated rail profile exceeds a predetermined wear limit forthe rail by: running the contact model to produce a subsequent simulatedloading; running the wear model to produce a subsequent simulated wearprofile based on the subsequent simulated loading; and generating asubsequent updated rail profile by modifying the prior updated railprofile by the subsequent simulated wear profile and/or a subsequentgrinding profile; and calculating a wear time until the final updatedrail profile exceeds the predetermined wear limit; determining thepredicted rail profile having the longest wear time; and maintaining therail for at least the initial predetermined time period in accordancewith the set of maintenance parameters associated with the predictedrail profile having the longest wear time.
 2. The method of claim 1,wherein the at least one set of the plurality of sets of maintenanceparameters includes a first grinding protocol and a second grindingprotocol, the first grinding protocol including a first grindingoperation performed on the rail during the initial predetermined timeperiod, the second grinding profile including a second grindingoperation performed on the rail during a subsequent predetermined timeperiod, and further comprising generating a second updated rail profileof the subsequent updated rail profiles by modifying the updated railprofile by a second simulated wear profile of the subsequent wearprofiles and the second grinding profile.
 3. The method of claim 1,wherein the contact model further includes a system model of force andpressure profiles between multiple sets of wheels of the train car andthe train track and a wheel contact model of rolling contact forcesbetween the wheel of the train car and the rail.
 4. The method of claim1, wherein the simulated loading is divided into discrete time steps,and a defined load is simulated to travel a distance over the rail ineach time step, wherein the defined load is simulated to exert differentamounts of pressure across the rail in each time step due to asperitycontact between the rail and the wheel of the train car.
 5. The methodof claim 1, wherein the simulated wear profile includes a wear depthprofile and generating the updated rail profile includes subtracting thewear depth profile from the rail profile.
 6. The method of claim 1,wherein generating the contact model includes generating a finiteelement model based on the material properties of the rail, wherein thefinite element model includes a plurality of elements corresponding toportions of a grain structure of the rail and represents polycrystallineproperties of the rail, and wherein generating the finite element modelincludes generating a random microstructure instance using atessellation and meshing the random microstructure instance with aconvex polygon; and each element of the plurality of elements includesone or more functions defining a behavior of the material properties ofthe rail, the material properties including a brittleness of the rail ofthe train track.
 7. The method of claim 1, further comprisinggenerating, for each of the plurality of predicted rail profiles, a plotof the rail profile, updated rail profile, and subsequent updated railprofiles over time.
 8. The method of claim 1, further comprising, foreach iteration, regenerating the contact model of the interactionbetween the rail and a train based on the updated rail profile or thesubsequent updated rail profile, the train wheel profile, and estimatedtrain traffic on the rail during the subsequent predetermined timeperiod.
 9. The method of claim 1, further comprising, for eachiteration, regenerating the wear model based on the material propertiesand properties of the friction modifier on the rail during thesubsequent predetermined time period.
 10. The method of claim 9, whereinthe rail profile includes a crack profile representing one or morecracks in the rail of the train track, and further comprising:generating a crack growth model based on the rail profile and the crackprofile; running the crack growth model using the rail profile, thecrack profile, and the simulated loading to produce a simulated crackgrowth profile of the rail profile for the predetermined time period,wherein the simulated crack growth profile represents one or more formedor initiated cracks in the rail of the train track; and generating theupdated rail profile with an updated crack profile by modifying the railprofile by the simulated wear profile, the grinding profile, and thesimulated crack growth profile.
 11. The method of claim 10, furthercomprising repeating iteratively with the updated rail profile with theupdated crack profile and subsequent updated rail profiles withsubsequent updated crack profiles for corresponding subsequentpredetermined time periods the following steps: running the contactmodel to produce a subsequent simulated loading; running the wear modelto produce a subsequent simulated wear profile based on the subsequentsimulated loading; running the crack growth model to produce asubsequent simulated crack growth profile; and generating the subsequentupdated rail profile with the subsequent updated crack profile bymodifying an immediately prior updated rail profile by the subsequentsimulated wear profile and the subsequent simulated crack growthprofile; wherein the step of modeling wear in the rail is completed whena final subsequent updated rail profile exceeds a predetermined wearlimit for the rail or a final subsequent updated crack profile exceeds apredetermined crack growth fail limit.
 12. The method of claim 10,wherein the updated rail profile is produced by overlaying the simulatedcrack growth profile and the simulated wear profile onto the railprofile.
 13. The method of claim 12, wherein the simulated wear profileincludes an average wear depth, and the simulated crack growth profileincludes a maximum crack growth depth, and the method further comprisescalculating a recommended grinding profile having an average grindingdepth substantially equal to the difference between the maximum crackgrowth depth and the average wear depth.
 14. The method of claim 1,wherein the application of a friction modifier to be applied to the railincludes a distance between friction modifier applicators on the rail.15. A method for maintaining a train track, the method comprising:modeling wear in a rail of a train track due to an estimated traintraffic by: obtaining a train wheel profile of a train car; providingtwo or more sets of maintenance parameters, each set of maintenanceparameters including: a rail profile; grinding parameters; and railmaterial properties; wherein at least one pair of correspondingmaintenance parameters in the two or more sets of maintenance parametersis different from one another; for each of the two or more sets ofmaintenance parameters: generating a contact model of an interactionbetween the rail profile and a wheel of a train based on the railprofile, the train wheel profile, and estimated train traffic on therail; generating a wear model based on the material properties;performing a wear simulation using the rail profile for a predeterminedtime period of one month or less by: running the contact model toproduce a simulated loading; running the wear model to produce asimulated wear profile based on the simulated loading; and generating anupdated rail profile by modifying the rail profile by the simulated wearprofile and the grinding parameters; repeating the wear simulationiteratively for additional predetermined time periods using the updatedrail profile and subsequent updated rail profiles until a final updatedrail profile exceeds a predetermined wear limit for the rail; andcalculating a wear time until the final updated rail profile exceeds thepredetermined wear limit, wherein the wear time is at least one year;and comparing the wear times associated with each set of maintenanceparameters; generating a maintenance recommendation based on the weartimes associated with each set of maintenance parameters, whereingenerating the maintenance recommendation includes either i) comparing acost value over the wear time for each set of maintenance parameters,the cost value based on maintenance costs associated with thecorresponding set of maintenance parameters, and selecting a set ofmaintenance parameters having a lower cost value, or ii) selecting a setof maintenance parameters having the longest wear time; and grinding therail according to the grinding parameters of the maintenancerecommendation.
 16. The method of claim 15, wherein generating themaintenance recommendation includes selecting the set of maintenanceparameters having the lower cost value.
 17. The method of claim 15,wherein generating the maintenance recommendation includes selecting theset of maintenance parameters having the longest wear time.
 18. A methodfor maintaining a train track, the method comprising: modeling wear in arail of a train track due to an estimated train traffic by: configuringa computer-based system to predict wear in the rail of the train track,the computer-based system comprising: an input device operable toreceive material properties of the rail, a rail profile of the rail, anda set of maintenance parameters, including at least one of a grindingprofile for at least one grinding operation to be performed on the railto produce artificial wear or an application of a friction modifier tobe applied to the rail; an output device operable to convey wearinformation relating to the rail; memory operable to store the materialproperties of the rail, the rail profile of the rail, a train wheelprofile of a wheel of a train car, and computer-executable instructionsincluding wear prediction processes; and a processor; predicting wear inthe rail with the computer-based system according to the wear predictionprocesses of the computer-executable instructions, wherein thecomputer-executable instructions cause the processor to predict wear inthe rail by: generating a contact model of the interaction between therail and the train car based on the rail profile, the train wheelprofile, and the estimated train traffic on the rail; running thecontact model to produce a simulated loading on the rail for apredetermined time period using the rail profile; generating a wearmodel based on the material properties and/or properties of the frictionmodifier on the rail during the predetermined time; running the wearmodel using the rail profile and the simulated loading from the contactmodel to produce a simulated wear profile of the rail for thepredetermined time period; generating an updated rail profile bymodifying the rail profile by the simulated wear profile and/or thegrinding profile, wherein the computer-executable instructions cause theprocessor to repeat iteratively with the updated rail profile andsubsequent updated rail profiles for corresponding subsequentpredetermined time periods the following steps until a final subsequentupdated rail profile exceeds a predetermined wear limit for the rail:running the contact model to produce a subsequent simulated loading,wherein the predetermined time period of the contact model is one monthor less; running the wear model to produce a subsequent simulated wearprofile based on the subsequent simulated loading, wherein thepredetermined time period of the wear model is one month or less; andgenerating the subsequent updated rail profile by modifying the priorupdated rail profile by the subsequent simulated wear profile and thegrinding profile; and calculating a wear time until the final subsequentupdated rail profile is reached, wherein the wear time is at least oneyear; wherein predicting wear in the rail includes calculating acorresponding wear time for each of a plurality of sets of maintenanceparameters, the plurality of sets of maintenance parameters including afirst set of maintenance parameters and a second set of maintenanceparameters, a first wear time corresponding to the wear time until thefinal subsequent updated rail profile is reached based on the first setof maintenance parameters and a second wear time corresponding to thewear time until the final subsequent updated rail profile is reachedbased on the second set of maintenance parameters; andmaintenance-parameters-maintaining the rail according to one of thefirst set of maintenance parameters or the second set of maintenanceparameters having the longest wear time.
 19. The method of claim 18,wherein the input device is operable to receive the train wheel profileof the wheel of the train car and the estimated train traffic for therail.
 20. The method of claim 19, further comprising: generating anddisplaying with the output device a plot of the rail profile, theupdated rail profile, and any subsequent updated rail profiles overtime.